Robust H-infinity Control Of Discrete Singular Systems With Saturating Actuators

In the control systems, the ideal models are often studied for the controllers design without considering the characteristic of saturation of actuators. However, in the practical production process, due to the mechanical constraints and requirements of the production process, actuators usually have the non-linear dynamic characteristic of saturation. When the inputs of actuators reach the maximum limit, the systems are saturated and the further growth of inputs has no effect on the outputs of actuators. Saturation is able to reduce the dynamic performance of the systems, and even leads to the instability of the closed-loop systems. It has aroused more and more concern so that a solution is gained to deal with the issue of saturation of actuators. It should be noted that the research of the classical systems with saturating actuators has a lot of results, but the research of the generalized systems with saturating actuators has few achievements.The robust H-infinity control, robust stabilization and stabilization of discrete singular systems with saturating actuators are discussed in this paper. Firstly, the problem of stabilization is explored for discrete singular systems with saturating actuators. In terms of the algebraic method, the norm inequality property and the decomposing theorem of large-scale system, sufficient conditions are presented such that the close-loop systems are admissible. Meanwhile, procedures are developed to design the corresponding controllers. Secondly, the problem of robust stabilization is studied for discrete singular systems with saturating actuators. Based on the condition that discrete singular systems are admissible, by using the generalized Lyapunov function and linear matrix inequality method, sufficient conditions that the close-loop systems are admissible are established. Then sufficient conditions for the robust stabilization of discrete singular systems with saturating actuators are given in terms of the linear matrix inequality method. At the same time, state feedback controllers are designed by the feasible solution of the linear matrix inequality. Thirdly, the problem of robust H-infinity control is studied for discrete singular time-delay systems with saturating actuators. Based on the admissible criterion for discrete singular time-delay systems, in terms of generalized Lyapunov stability theorem, sufficient conditions are obtained such that close-loop systems are admissible and have the H-infinity performance. Then by means of linear matrix inequality method, state feedback controllers are designed and sufficient conditions are gained to guarantee that systems are admissible and have the H-infinity performance.The concept of saturation is firstly extended to discrete singular systems and the stabilization, robust stabilization and robust H-infinity control of discrete singular systems with saturating actuators are mainly considered in this paper. The examples are given correspondingly to demonstrate the effectiveness of the conclusions, and the corresponding controllers are also presented.